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+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <meta name="viewport" content="width=device-width, initial-scale=1.0">
+    <title>Draw the Great Circle Path</title>
+    <link rel="stylesheet" href="https://unpkg.com/leaflet@1.9.4/dist/leaflet.css" integrity="sha256-p4NxAoJBhIIN+hmNHrzRCf9tD/miZyoHS5obTRR9BMY=" crossorigin="" />
+    <style>
+        body {
+            font-family: Arial, sans-serif;
+            margin: 0;
+            padding: 0;
+        }
+        #map {
+            height: 400px;
+            width: 80%;
+            margin: 20px auto;
+            border: 1px solid #ccc;
+        }
+        .container {
+            width: 80%;
+            margin: 20px auto;
+        }
+        h1, h2 {
+            text-align: center;
+        }
+        h2 {
+            margin-top: 30px;
+        }
+        pre {
+            background-color: #f5f5f5;
+            padding: 15px;
+            border-radius: 5px;
+            overflow-x: auto;
+        }
+        code {
+            font-family: 'Courier New', Courier, monospace;
+        }
+        .subtitle {
+            text-align: center;
+            margin-bottom: 20px;
+        }
+        .form-container {
+            display: flex;
+            justify-content: center;
+            align-items: center;
+            margin-bottom: 20px;
+        }
+        .form-group {
+            margin-right: 15px;
+        }
+        label {
+            display: block;
+            margin-bottom: 5px;
+        }
+        input[type="number"] {
+            width: 100px;
+        }
+        .leaflet-div-icon {
+            background: transparent;
+            border: none;
+        }
+
+        .triangle {
+            width: 0;
+            height: 0;
+            border-left: 8px solid transparent;
+            border-right: 8px solid transparent;
+            border-bottom: 16px solid purple;
+        }
+    </style>
+</head>
+<body>
+    <div class="container">
+        <h1>Drawing the Great Circle on a Leaflet Map</h1>
+        <p class="subtitle">By Dr. Dan Ames - Jan 23, 2025</p>
+
+        <div id="map"></div>
+
+        <h2>Enter the Start and End Coordinates</h2>
+        <div class="form-container">
+          <div class="form-group">
+              <label for="start_latitude">Start Latitude:</label>
+              <input type="number" id="start_latitude" name="start_latitude" value="40.0">
+          </div>
+          <div class="form-group">
+              <label for="start_longitude">Start Longitude:</label>
+              <input type="number" id="start_longitude" name="start_longitude" value="-111.0">
+          </div>
+          <div class="form-group">
+              <label for="end_latitude">End Latitude:</label>
+              <input type="number" id="end_latitude" name="end_latitude" value="39.0">
+          </div>
+          <div class="form-group">
+              <label for="end_longitude">End Longitude:</label>
+              <input type="number" id="end_longitude" name="end_longitude" value="1.0">
+          </div>
+          
+          <button id="submit-button">Draw Points and Great Circle</button>
+        </div>
+        <div id="results">
+          Results: 
+        </div>
+
+
+    <script src="https://unpkg.com/leaflet@1.9.4/dist/leaflet.js" integrity="sha256-20nQCchB9co0qIjJZRGuk2/Z9VM+kNiyxNV1lvTlZBo=" crossorigin=""></script>
+    <script>
+        // Initialize the map
+        var map = L.map('map').setView([39.0, -45.0], 3); // Centered on Utah
+
+        // Add a tile layer (base map) from OpenStreetMap
+        L.tileLayer('https://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png', {
+            attribution: '&copy; <a href="https://www.openstreetmap.org/copyright">OpenStreetMap</a> contributors'
+        }).addTo(map);
+
+        // Function to create a triangle marker
+        function createTriangleIcon() {
+            return L.divIcon({
+                className: 'triangle',
+                iconSize: [16, 16]
+            });
+        }
+
+        //Function to compute the distance between two points using the Haversine formula
+        function compute_distance(lat1,lng1,lat2,lng2){
+            //convert inputs to radians
+            const rad_lat1 = lat1 * Math.PI/180;
+            const rad_lng1 = lng1 * Math.PI/180;
+            const rad_lat2 = lat2 * Math.PI/180;
+            const rad_lng2 = lng2 * Math.PI/180;
+            
+            //Differences in coordinates
+            const dLat = rad_lat2 - rad_lat1;
+            const dLon = rad_lng2 - rad_lng1;
+            
+            //Earth's radius in km (estimated)
+            const R = 6371; 
+            
+            //Haversine formula                                      
+            const a = (Math.sin(dLat/2))**2 + Math.cos(rad_lat1) * Math.cos(rad_lat2) * (Math.sin((dLon)/2))**2;
+            const c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
+            const distance = R * c;
+            //a = sin²(Δφ/2) + cos(φ₁) * cos(φ₂) * sin²(Δλ/2)
+            //c = 2 * atan2(√a, √(1-a))
+            //d = R * c
+                                    
+            //Write the resulting distance
+            document.getElementById("results").innerHTML = "Distance = " + distance + " km";
+        }       
+
+
+         // Function to draw a great circle line connecting the two points
+        function great_circle(lat1, lng1, lat2, lng2) {
+            // Convert inputs to radians
+            const rad_lat1 = lat1 * Math.PI / 180;
+            const rad_lng1 = lng1 * Math.PI / 180;
+            const rad_lat2 = lat2 * Math.PI / 180;
+            const rad_lng2 = lng2 * Math.PI / 180;
+
+            // Calculate the angular distance (δ) between the two points using the Haversine formula
+            const dLon = rad_lng2 - rad_lng1;
+            const dLat = rad_lat2 - rad_lat1;
+            const a = Math.sin(dLat / 2) ** 2 + Math.cos(rad_lat1) * Math.cos(rad_lat2) * Math.sin(dLon / 2) ** 2;
+            const angular_distance = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a)); // This is 'c' in your equations
+
+            // Divide the angular distance into 10 segments
+            const num_segments = 100; // Increased for smoother line
+            const segment_angle = angular_distance / num_segments;
+
+            // Generate points along the great circle
+            const points = [];
+            for (let i = 0; i <= num_segments; i++) {
+                const f = i / num_segments;
+
+                // Calculate intermediate latitude (φ) and longitude (λ)
+                const A = Math.sin((1 - f) * angular_distance) / Math.sin(angular_distance);
+                const B = Math.sin(f * angular_distance) / Math.sin(angular_distance);
+                const x = A * Math.cos(rad_lat1) * Math.cos(rad_lng1) + B * Math.cos(rad_lat2) * Math.cos(rad_lng2);
+                const y = A * Math.cos(rad_lat1) * Math.sin(rad_lng1) + B * Math.cos(rad_lat2) * Math.sin(rad_lng2);
+                const z = A * Math.sin(rad_lat1) + B * Math.sin(rad_lat2);
+                const new_lat = Math.atan2(z, Math.sqrt(x ** 2 + y ** 2));
+                const new_lng = Math.atan2(y, x);
+
+                points.push([new_lat * 180 / Math.PI, new_lng * 180 / Math.PI]);
+            }
+
+            // Draw the great circle line
+            const polyline = L.polyline(points, { color: 'red' }).addTo(map);
+        }
+        
+        
+        // Add marker on form submission
+        document.getElementById('submit-button').addEventListener('click', function() {
+            var start_lat = parseFloat(document.getElementById('start_latitude').value);
+            var start_lng = parseFloat(document.getElementById('start_longitude').value);
+            var end_lat = parseFloat(document.getElementById('end_latitude').value);
+            var end_lng = parseFloat(document.getElementById('end_longitude').value);
+
+            if (!isNaN(start_lat) && !isNaN(start_lng) && !isNaN(end_lat) && !isNaN(end_lng)) {
+                var startMarker = L.marker([start_lat, start_lng], {
+                    icon: createTriangleIcon()
+                }).addTo(map);
+                startMarker.bindPopup("Start Point<br>[" + start_lat + ", " + start_lng + "]");
+
+                var endMarker = L.marker([end_lat, end_lng], {
+                    icon: createTriangleIcon()
+                }).addTo(map);
+                endMarker.bindPopup("End Point<br>[" + end_lat + ", " + end_lng + "]");
+
+                //compute the distance between the two points                       
+                compute_distance(start_lat,start_lng,end_lat,end_lng);
+                great_circle(start_lat,start_lng,end_lat,end_lng);
+
+            } else {
+                alert('Please enter valid coordinates.');
+            }
+        });
+
+    </script>
+    </div>
+</body>
+</html>
